Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C8×Dic62 | C2 | semidirect |
| 4. #14520800 | C2 | semidirect |
| 5. #14520781 | C2 | semidirect |
| 7. C82×C31 | C2 | semidirect |
| 39. #92470 | C8 | direct (N × H) |
| 53. Dic62 | C2×C8 | semidirect |
| 57. C8×C31 | C2×C8 | semidirect |
| 58. C8×C31 | SD16 | semidirect |
| 80. C82 | D31 | semidirect |
| 100. C31 | C8×SD16 | semidirect |
| 137. C8 | C8×D31 | semidirect |
| 138. C8 | #92470 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic62 | 2 |
| C4×#92470 | 2 |
| C8×D124 | 2 |
| #14520800 | 2 |
| #14520781 | 2 |
| #14520778 | 2 |
| C82×C31 | 2 |
| C8×SD16 | 31 |